Project : Aircraft Predictive Maintenance

Exploratory Data Analysis

Author: Arnaud Duigou Date: 22-Dec-2023 Goal: - Use ML to redict the risk of failure of a machine (i.e. Aircraft turbine) based on sensor values monitoring. - Trigger-off preventive maintenance activities for cause

1. Load packages and dependencies

# Dependencies
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import warnings

# Jupyter Notebook Options
plt.style.use('ggplot')
pd.set_option('display.max_columns', None) 
pd.set_option('display.max_rows', 500) 
pd.set_option('display.expand_frame_repr', False)
%matplotlib inline
warnings.filterwarnings('ignore')

2. About the dataset

2.1 Dataset Loading

col_names = ['id','cycle','setting1','setting2','setting3','s1','s2','s3','s4','s5','s6','s7','s8','s9',
             's10','s11','s12','s13','s14','s15','s16','s17','s18','s19','s20','s21']

parameters_dict = {
    'id':'engine',
    's1':"(Fan inlet temperature) (◦R)",
    's2':"(LPC outlet temperature) (◦R)",
    's3':"(HPC outlet temperature) (◦R)",
    's4':"(LPT outlet temperature) (◦R)",
    's5':"(Fan inlet Pressure) (psia)",
    's6':"(bypass-duct pressure) (psia)",
    's7':"(HPC outlet pressure) (psia)",
    's8':"(Physical fan speed) (rpm)",
    's9':"(Physical core speed) (rpm)",
    's10':"(Engine pressure ratio(P50/P2)",
    's11':"(HPC outlet Static pressure) (psia)",
    's12':"(Ratio of fuel flow to Ps30) (pps/psia)",
    's13':"(Corrected fan speed) (rpm)",
    's14':"(Corrected core speed) (rpm)",
    's15':"(Bypass Ratio) ",
    's16':"(Burner fuel-air ratio)",
    's17':"(Bleed Enthalpy)",
    's18':"(Required fan speed)",
    's19':"(Required fan conversion speed)",
    's20':"(High-pressure turbines Cool air flow)",
    's21':"(Low-pressure turbines Cool air flow)"
}

df_train_raw = pd.read_csv('PM_train.txt', sep = ' ', header=None)
df_train_raw.drop([26,27], axis=1, inplace=True)
df_train_raw.columns = col_names
df_train_raw.head()

	id	cycle	setting1	setting2	setting3	s1	s2	s3	s4	s5	s6	s7	s8	s9	s10	s11	s12	s13	s14	s15	s16	s17	s18	s19	s20	s21
0	1	1	-0.0007	-0.0004	100.0	518.67	641.82	1589.70	1400.60	14.62	21.61	554.36	2388.06	9046.19	1.3	47.47	521.66	2388.02	8138.62	8.4195	0.03	392	2388	100.0	39.06	23.4190
1	1	2	0.0019	-0.0003	100.0	518.67	642.15	1591.82	1403.14	14.62	21.61	553.75	2388.04	9044.07	1.3	47.49	522.28	2388.07	8131.49	8.4318	0.03	392	2388	100.0	39.00	23.4236
2	1	3	-0.0043	0.0003	100.0	518.67	642.35	1587.99	1404.20	14.62	21.61	554.26	2388.08	9052.94	1.3	47.27	522.42	2388.03	8133.23	8.4178	0.03	390	2388	100.0	38.95	23.3442
3	1	4	0.0007	0.0000	100.0	518.67	642.35	1582.79	1401.87	14.62	21.61	554.45	2388.11	9049.48	1.3	47.13	522.86	2388.08	8133.83	8.3682	0.03	392	2388	100.0	38.88	23.3739
4	1	5	-0.0019	-0.0002	100.0	518.67	642.37	1582.85	1406.22	14.62	21.61	554.00	2388.06	9055.15	1.3	47.28	522.19	2388.04	8133.80	8.4294	0.03	393	2388	100.0	38.90	23.4044

df_test_raw = pd.read_csv('PM_test.txt', sep = ' ', header=None)
df_test_raw.drop([26,27], axis=1, inplace=True)
df_test_raw.columns = col_names
df_test_raw.head()

	id	cycle	setting1	setting2	setting3	s1	s2	s3	s4	s5	s6	s7	s8	s9	s10	s11	s12	s13	s14	s15	s16	s17	s18	s19	s20	s21
0	1	1	0.0023	0.0003	100.0	518.67	643.02	1585.29	1398.21	14.62	21.61	553.90	2388.04	9050.17	1.3	47.20	521.72	2388.03	8125.55	8.4052	0.03	392	2388	100.0	38.86	23.3735
1	1	2	-0.0027	-0.0003	100.0	518.67	641.71	1588.45	1395.42	14.62	21.61	554.85	2388.01	9054.42	1.3	47.50	522.16	2388.06	8139.62	8.3803	0.03	393	2388	100.0	39.02	23.3916
2	1	3	0.0003	0.0001	100.0	518.67	642.46	1586.94	1401.34	14.62	21.61	554.11	2388.05	9056.96	1.3	47.50	521.97	2388.03	8130.10	8.4441	0.03	393	2388	100.0	39.08	23.4166
3	1	4	0.0042	0.0000	100.0	518.67	642.44	1584.12	1406.42	14.62	21.61	554.07	2388.03	9045.29	1.3	47.28	521.38	2388.05	8132.90	8.3917	0.03	391	2388	100.0	39.00	23.3737
4	1	5	0.0014	0.0000	100.0	518.67	642.51	1587.19	1401.92	14.62	21.61	554.16	2388.01	9044.55	1.3	47.31	522.15	2388.03	8129.54	8.4031	0.03	390	2388	100.0	38.99	23.4130

df_truth = pd.read_csv('PM_truth.txt', sep = ' ', header=None)
df_truth.drop([1], axis=1, inplace=True)
df_truth.columns = ['ttf']
df_truth.head()

	ttf
0	112
1	98
2	69
3	82
4	91

2.2 Dataset description

Data Source

___Training Data:___ The aircraft engine run-to-failure data. download trianing data
___Test Data:___ The aircraft engine operating data without failure events recorded. download test data
___Ground Truth Data:___ The true remaining cycles for each engine in the testing data. download truth data

Data Columns

• id: is the engine ID, ranging from 1 to 100
• cycle: per engine sequence, starts from 1 to the cycle number where failure had happened (trining data only) • setting1 to setting3: engine operational settings
• s1 to s21: sensors measurements

Data Source Training Data: The aircraft engine run-to-failure data. download trianing data Test Data: The aircraft engine operating data without failure events recorded. download test data

• id: is the engine ID, ranging from 1 to 100 • cycle: per engine sequence, starts from 1 to the cycle number where failure had happened (trining data only) • setting1 to setting3: engine operational settings • s1 to s21: sensors measurements

Same as training data, there are 100 engines, each engine has between 1 to 303 cycles (average of 76 cycles per engine). But this time, failure cycle was not provided.

Failure events for test data - remaining cycles before failure (TTF) - were provided in a separate truth file.

To get meaningful test data, we need to merge the truth data (TTF) with last cycle for each engine in the test data. This will give us a test set of 100 engines with their TTF data. Will do that later when we create regression and classification labels for both training and test data.

But now let us add some features to smooth the sensors reading: rolling average and rolling standard deviation.

There are 100 engines. each engine has between 1 to 362 cycles (average of 108 cycles per engine). The last cycle for each engine represents the cycle when failure had happened.

Same as training data, there are 100 engines, each engine has between 1 to 303 cycles (average of 76 cycles per engine). But this time, failure cycle was not provided.

Failure events for test data - remaining cycles before failure (TTF) - were provided in a separate truth file.

2.3 Feature Extraction

import functions_library as fl

df_train_fx = fl.add_features(df_train_raw, 5)
df_train = fl.prepare_train_data (df_train_fx, 30)
df_train.to_csv('train.csv', index=False)

df_test_fx = fl.add_features(df_test_raw, 5)
df_test = fl.prepare_test_data (df_test_fx, df_truth, 30)
df_test.to_csv('test.csv', index=False)

# Import train / test dataset
train = pd.read_csv('train.csv')
test = pd.read_csv('test.csv')

3. Exploratory Data Analysis

3.1 Unviariate Analysis

The first step of a machine learning project is to perform an EDA (Exploratory Data Analysis) in order to grasp the main dynamics of the data. This step is interesting to perform a robust Feature Engineering.

train.head()

	id	cycle	setting1	setting2	setting3	s1	s2	s3	s4	s5	s6	s7	s8	s9	s10	s11	s12	s13	s14	s15	s16	s17	s18	s19	s20	s21	av1	av2	av3	av4	av5	av6	av7	av8	av9	av10	av11	av12	av13	av14	av15	av16	av17	av18	av19	av20	av21	sd1	sd2	sd3	sd4	sd5	sd6	sd7	sd8	sd9	sd10	sd11	sd12	sd13	sd14	sd15	sd16	sd17	sd18	sd19	sd20	sd21	ttf	label_bnc	label_mcc
0	1	1	-0.0007	-0.0004	100.0	518.67	641.82	1589.70	1400.60	14.62	21.61	554.36	2388.06	9046.19	1.3	47.47	521.66	2388.02	8138.62	8.4195	0.03	392	2388	100.0	39.06	23.4190	518.67	641.820000	1589.700000	1400.600000	14.62	21.61	554.360000	2388.0600	9046.190000	1.3	47.470	521.660	2388.020	8138.620000	8.419500	0.03	392.000000	2388.0	100.0	39.060000	23.419000	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.0	0.0	0.000000	0.000000	191	0	0
1	1	2	0.0019	-0.0003	100.0	518.67	642.15	1591.82	1403.14	14.62	21.61	553.75	2388.04	9044.07	1.3	47.49	522.28	2388.07	8131.49	8.4318	0.03	392	2388	100.0	39.00	23.4236	518.67	641.985000	1590.760000	1401.870000	14.62	21.61	554.055000	2388.0500	9045.130000	1.3	47.480	521.970	2388.045	8135.055000	8.425650	0.03	392.000000	2388.0	100.0	39.030000	23.421300	0.0	0.233345	1.499066	1.796051	0.0	0.0	0.431335	0.014142	1.499066	0.0	0.014142	0.438406	0.035355	5.041671	0.008697	0.0	0.000000	0.0	0.0	0.042426	0.003253	190	0	0
2	1	3	-0.0043	0.0003	100.0	518.67	642.35	1587.99	1404.20	14.62	21.61	554.26	2388.08	9052.94	1.3	47.27	522.42	2388.03	8133.23	8.4178	0.03	390	2388	100.0	38.95	23.3442	518.67	642.106667	1589.836667	1402.646667	14.62	21.61	554.123333	2388.0600	9047.733333	1.3	47.410	522.120	2388.040	8134.446667	8.423033	0.03	391.333333	2388.0	100.0	39.003333	23.395600	0.0	0.267644	1.918654	1.850009	0.0	0.0	0.327159	0.020000	4.632023	0.0	0.121655	0.404475	0.026458	3.717450	0.007640	0.0	1.154701	0.0	0.0	0.055076	0.044573	189	0	0
3	1	4	0.0007	0.0000	100.0	518.67	642.35	1582.79	1401.87	14.62	21.61	554.45	2388.11	9049.48	1.3	47.13	522.86	2388.08	8133.83	8.3682	0.03	392	2388	100.0	38.88	23.3739	518.67	642.167500	1588.075000	1402.452500	14.62	21.61	554.205000	2388.0725	9048.170000	1.3	47.340	522.305	2388.050	8134.292500	8.409325	0.03	391.500000	2388.0	100.0	38.972500	23.390175	0.0	0.250117	3.855909	1.559645	0.0	0.0	0.313103	0.029861	3.881555	0.0	0.171659	0.495950	0.029439	3.050906	0.028117	0.0	1.000000	0.0	0.0	0.076322	0.037977	188	0	0
4	1	5	-0.0019	-0.0002	100.0	518.67	642.37	1582.85	1406.22	14.62	21.61	554.00	2388.06	9055.15	1.3	47.28	522.19	2388.04	8133.80	8.4294	0.03	393	2388	100.0	38.90	23.4044	518.67	642.208000	1587.030000	1403.206000	14.62	21.61	554.164000	2388.0700	9049.566000	1.3	47.328	522.282	2388.048	8134.194000	8.413340	0.03	391.800000	2388.0	100.0	38.958000	23.393020	0.0	0.234776	4.075678	2.159440	0.0	0.0	0.286234	0.026458	4.587366	0.0	0.151063	0.432574	0.025884	2.651326	0.025953	0.0	1.095445	0.0	0.0	0.073621	0.033498	187	0	0

train = fl.remove_columns_with_same_min_max(train)

# train.rename(columns=parameters_dict, inplace=True)

fl.custom_describe(train)

	mean	std	min	25%	50%	75%	max	count	zero_count	nan_count	skewness	kurtosis
id	51.506568	29.227633	1.0000	26.000000	52.000000	77.000000	100.000000	20631.0	0.0	0.0	-0.067810	-1.219819
cycle	108.807862	68.880990	1.0000	52.000000	104.000000	156.000000	362.000000	20631.0	0.0	0.0	0.499868	-0.218777
setting1	-0.000009	0.002187	-0.0087	-0.001500	0.000000	0.001500	0.008700	20631.0	413.0	0.0	-0.024764	-0.009420
setting2	0.000002	0.000293	-0.0006	-0.000200	0.000000	0.000300	0.000600	20631.0	2070.0	0.0	0.009084	-1.130464
s2	642.680934	0.500053	641.2100	642.325000	642.640000	643.000000	644.530000	20631.0	0.0	0.0	0.316503	-0.112307
s3	1590.523119	6.131150	1571.0400	1586.260000	1590.100000	1594.380000	1616.910000	20631.0	0.0	0.0	0.308923	0.007469
s4	1408.933782	9.000605	1382.2500	1402.360000	1408.040000	1414.555000	1441.490000	20631.0	0.0	0.0	0.443162	-0.163932
s6	21.609803	0.001389	21.6000	21.610000	21.610000	21.610000	21.610000	20631.0	0.0	0.0	-6.916310	45.835345
s7	553.367711	0.885092	549.8500	552.810000	553.440000	554.010000	556.060000	20631.0	0.0	0.0	-0.394300	-0.158202
s8	2388.096652	0.070985	2387.9000	2388.050000	2388.090000	2388.140000	2388.560000	20631.0	0.0	0.0	0.479376	0.332777
s9	9065.242941	22.082880	9021.7300	9053.100000	9060.660000	9069.420000	9244.590000	20631.0	0.0	0.0	2.555179	9.376118
s11	47.541168	0.267087	46.8500	47.350000	47.510000	47.700000	48.530000	20631.0	0.0	0.0	0.469295	-0.172441
s12	521.413470	0.737553	518.6900	520.960000	521.480000	521.950000	523.380000	20631.0	0.0	0.0	-0.442375	-0.145172
s13	2388.096152	0.071919	2387.8800	2388.040000	2388.090000	2388.140000	2388.560000	20631.0	0.0	0.0	0.469758	0.386859
s14	8143.752722	19.076176	8099.9400	8133.245000	8140.540000	8148.310000	8293.720000	20631.0	0.0	0.0	2.372381	8.852228
s15	8.442146	0.037505	8.3249	8.414900	8.438900	8.465600	8.584800	20631.0	0.0	0.0	0.388230	-0.121691
s17	393.210654	1.548763	388.0000	392.000000	393.000000	394.000000	400.000000	20631.0	0.0	0.0	0.353100	-0.039455
s20	38.816271	0.180746	38.1400	38.700000	38.830000	38.950000	39.430000	20631.0	0.0	0.0	-0.358419	-0.113093
s21	23.289705	0.108251	22.8942	23.221800	23.297900	23.366800	23.618400	20631.0	0.0	0.0	-0.350349	-0.117302
av2	642.668177	0.410199	641.4500	642.366000	642.624000	642.918000	644.020000	20631.0	0.0	0.0	0.479614	-0.208867
av3	1590.371974	4.864211	1573.0200	1586.869000	1589.760000	1593.192000	1608.070000	20631.0	0.0	0.0	0.560107	-0.017956
av4	1408.670908	8.032418	1387.3800	1402.633000	1407.712000	1413.483000	1432.984000	20631.0	0.0	0.0	0.532997	-0.273388
av6	21.609798	0.000734	21.6000	21.610000	21.610000	21.610000	21.610000	20631.0	0.0	0.0	-4.610210	29.020033
av7	553.392492	0.787783	550.8100	552.934000	553.460000	553.996000	555.370000	20631.0	0.0	0.0	-0.479222	-0.266622
av8	2388.094887	0.064036	2387.9200	2388.046000	2388.092000	2388.134000	2388.326000	20631.0	0.0	0.0	0.522656	0.100060
av9	9064.827207	20.825535	9027.6520	9053.788000	9060.288000	9068.334000	9223.844000	20631.0	0.0	0.0	2.592280	9.451631
av11	47.533241	0.244682	46.9300	47.348000	47.510000	47.676000	48.274000	20631.0	0.0	0.0	0.514913	-0.277990
av12	521.434437	0.669201	519.2240	521.046000	521.488000	521.944000	522.970000	20631.0	0.0	0.0	-0.499478	-0.251130
av13	2388.094344	0.064908	2387.9300	2388.046000	2388.092000	2388.132000	2388.338000	20631.0	0.0	0.0	0.492525	0.058653
av14	8143.460137	18.072103	8103.4660	8133.375000	8140.468000	8147.797000	8281.152000	20631.0	0.0	0.0	2.370463	8.766225
av15	8.441132	0.032072	8.3303	8.416830	8.437720	8.459970	8.542420	20631.0	0.0	0.0	0.537446	-0.210313
av17	393.169949	1.263436	390.0000	392.200000	393.000000	393.800000	397.600000	20631.0	0.0	0.0	0.540343	-0.121566
av20	38.821209	0.152667	38.3260	38.730000	38.838000	38.934000	39.270000	20631.0	0.0	0.0	-0.492091	-0.209058
av21	23.292606	0.091651	23.0114	23.238740	23.301540	23.360810	23.534900	20631.0	0.0	0.0	-0.502557	-0.210533
sd2	0.282887	0.105588	0.0000	0.207437	0.276622	0.349614	0.783913	20631.0	102.0	0.0	0.343976	0.120458
sd3	3.743819	1.405689	0.0000	2.756107	3.669396	4.637603	12.445079	20631.0	100.0	0.0	0.349888	0.305709
sd4	3.772323	1.402446	0.0000	2.784935	3.703867	4.677819	15.259364	20631.0	100.0	0.0	0.337459	0.469149
sd6	0.000387	0.001291	0.0000	0.000000	0.000000	0.000000	0.007071	20631.0	18912.0	0.0	3.066845	7.562016
sd7	0.379234	0.145381	0.0000	0.276695	0.369486	0.473777	1.350444	20631.0	100.0	0.0	0.358557	0.274632
sd8	0.028255	0.010881	0.0000	0.020736	0.027749	0.035071	0.200699	20631.0	110.0	0.0	0.930979	8.738667
sd9	3.946680	1.513374	0.0000	2.884196	3.824288	4.899879	12.694602	20631.0	100.0	0.0	0.430050	0.365064
sd11	0.095131	0.035433	0.0000	0.070000	0.092844	0.118025	0.247245	20631.0	101.0	0.0	0.330156	0.128424
sd12	0.281756	0.105403	0.0000	0.207244	0.274918	0.348482	0.898026	20631.0	101.0	0.0	0.374051	0.309839
sd13	0.028451	0.011049	0.0000	0.020736	0.027749	0.035355	0.220068	20631.0	118.0	0.0	1.150325	12.700276
sd14	3.016360	1.143912	0.0000	2.219386	2.939243	3.715888	9.919746	20631.0	100.0	0.0	0.489364	0.735085
sd15	0.018802	0.007103	0.0000	0.013724	0.018365	0.023380	0.065761	20631.0	100.0	0.0	0.371387	0.347628
sd17	0.885173	0.341989	0.0000	0.547723	0.836660	1.140175	2.828427	20631.0	460.0	0.0	0.245099	0.546409
sd20	0.094636	0.034867	0.0000	0.070071	0.092736	0.117132	0.325269	20631.0	103.0	0.0	0.303100	0.154156
sd21	0.056483	0.020669	0.0000	0.041825	0.055555	0.069839	0.187313	20631.0	100.0	0.0	0.326198	0.445241
ttf	107.807862	68.880990	0.0000	51.000000	103.000000	155.000000	361.000000	20631.0	100.0	0.0	0.499868	-0.218777
label_bnc	0.150259	0.357334	0.0000	0.000000	0.000000	0.000000	1.000000	20631.0	17531.0	0.0	1.957547	1.831991
label_mcc	0.227813	0.575358	0.0000	0.000000	0.000000	0.000000	2.000000	20631.0	17531.0	0.0	2.389476	4.237983

# train.select_dtypes(include='number').columns.to_list()

col_to_analyze = ['setting1','setting2','s2','s3','s4','s6','s7','s8','s9',
                  's11','s12','s13','s14','s15','s17','s20','s21', 'ttf']

# col_to_analyze = ['cycle',
#  'setting1',
#  'setting2',
#  '(LPC outlet temperature) (◦R)',
#  '(HPC outlet temperature) (◦R)',
#  '(LPT outlet temperature) (◦R)',
#  '(bypass-duct pressure) (psia)',
#  '(HPC outlet pressure) (psia)',
#  '(Physical fan speed) (rpm)',
#  '(Physical core speed) (rpm)',
#  '(HPC outlet Static pressure) (psia)',
#  '(Ratio of fuel flow to Ps30) (pps/psia)',
#  '(Corrected fan speed) (rpm)',
#  '(Corrected core speed) (rpm)',
#  '(Bypass Ratio) ',
#  '(Bleed Enthalpy)',
#  '(High-pressure turbines Cool air flow)',
#  '(Low-pressure turbines Cool air flow)', 'ttf']

We can see that the value of several sensor are stable and not moving. We can remove these features

fl.plot_histograms(train[col_to_analyze])

# train['s9'].mean()

# Log transformation
# for col in ['s6', 's9', 's14']:
#     train[col] = train[col].apply(np.log)
#     test[col] = test[col].apply(np.log)

['s12', 's7', 's21', 's20', 's6', 's14', 's9', 's13', 's8', 's3', 's17', 's2', 's15', 's4', 's11'] could be target for feature selection during modeling since their correlation with TTF is higher than other features.

Let us disply this correlation in heatmap

There is a very high correlation (> 0.8) between some features: (s14, s9), (s11, s4), (s11, s7), (s11, s12), (s4, s12), (s8,s13), (s7, s12)
This may hurt the performance of some ML algorithms.

So, some of the above features will be target for removal in feature selection. Some algorithm are struggled with colinearity.

# Create a function to explore the time series plot each sensor selecting random sample engines
def plot_time_series(s):
    
    """Plot time series of a single sensor for 10 random sample engines.
    
        Args:
        s (str): The column name of the sensor to be plotted.

    Returns:
        plots
        
    """
    
    fig, axes = plt.subplots(10, 1, sharex=True, figsize = (15, 15))
    fig.suptitle(s + ' time series / cycle', fontsize=15)
    
    #np.random.seed(12345)
    select_engines = np.random.choice(range(1,101), 10, replace=False).tolist()
    
    for e_id in select_engines:
        df = train[['cycle', s]][train.id == e_id]
        i = select_engines.index(e_id)
        axes[i].plot(df['cycle'],df[s])
        axes[i].set_ylabel('engine ' + str(e_id))
        axes[i].set_xlabel('cycle')
        #axes[i].set_title('engine ' + str(e_id), loc='right')

    #plt.tight_layout()
    plt.subplots_adjust(wspace=0, hspace=0)
    plt.show()

plot_time_series('s9')

3.2 Bivariate & Correlation Analysis

correl_featurs = ['setting1','setting2','s2','s3','s4','s6','s7','s8','s9','s11','s12','s13','s14','s15','s17','s20','s21']
correl_featurs_lbl = correl_featurs + ['ttf']

# col_to_analyze = ['cycle',
#  'setting1',
#  'setting2',
#  '(LPC outlet temperature) (◦R)',
#  '(HPC outlet temperature) (◦R)',
#  '(LPT outlet temperature) (◦R)',
#  '(bypass-duct pressure) (psia)',
#  '(HPC outlet pressure) (psia)',
#  '(Physical fan speed) (rpm)',
#  '(Physical core speed) (rpm)',
#  '(HPC outlet Static pressure) (psia)',
#  '(Ratio of fuel flow to Ps30) (pps/psia)',
#  '(Corrected fan speed) (rpm)',
#  '(Corrected core speed) (rpm)',
#  '(Bypass Ratio) ',
#  '(Bleed Enthalpy)',
#  '(High-pressure turbines Cool air flow)',
#  '(Low-pressure turbines Cool air flow)', 'ttf']

# train.rename(columns=parameters_dict, inplace=True)

# correl_featurs_lbl = col_to_analyze

# plot a heatmap to display +ve and -ve correlation among features and regression label:
cm = np.corrcoef(train[correl_featurs_lbl].values.T)
sns.set(font_scale=1.0)
fig = plt.figure(figsize=(10, 8))
hm = sns.clustermap(cm, cbar=True, annot=True, square=True, fmt='.2f', annot_kws={'size': 8}, 
                    yticklabels=correl_featurs_lbl, xticklabels=correl_featurs_lbl, cmap="vlag")
plt.title('Features Correlation Heatmap')
plt.show()

<Figure size 1000x800 with 0 Axes>

# from pandas.plotting import scatter_matrix

#create scatter matrix to disply relatiohships and distribution among features and regression label
# scatter_matrix(train[correl_featurs_lbl], alpha=0.2, figsize=(20, 20), diagonal='kde')

array([[<Axes: xlabel='setting1', ylabel='setting1'>,
        <Axes: xlabel='setting2', ylabel='setting1'>,
        <Axes: xlabel='s2', ylabel='setting1'>,
        <Axes: xlabel='s3', ylabel='setting1'>,
        <Axes: xlabel='s4', ylabel='setting1'>,
        <Axes: xlabel='s6', ylabel='setting1'>,
        <Axes: xlabel='s7', ylabel='setting1'>,
        <Axes: xlabel='s8', ylabel='setting1'>,
        <Axes: xlabel='s9', ylabel='setting1'>,
        <Axes: xlabel='s11', ylabel='setting1'>,
        <Axes: xlabel='s12', ylabel='setting1'>,
        <Axes: xlabel='s13', ylabel='setting1'>,
        <Axes: xlabel='s14', ylabel='setting1'>,
        <Axes: xlabel='s15', ylabel='setting1'>,
        <Axes: xlabel='s17', ylabel='setting1'>,
        <Axes: xlabel='s20', ylabel='setting1'>,
        <Axes: xlabel='s21', ylabel='setting1'>,
        <Axes: xlabel='ttf', ylabel='setting1'>],
       [<Axes: xlabel='setting1', ylabel='setting2'>,
        <Axes: xlabel='setting2', ylabel='setting2'>,
        <Axes: xlabel='s2', ylabel='setting2'>,
        <Axes: xlabel='s3', ylabel='setting2'>,
        <Axes: xlabel='s4', ylabel='setting2'>,
        <Axes: xlabel='s6', ylabel='setting2'>,
        <Axes: xlabel='s7', ylabel='setting2'>,
        <Axes: xlabel='s8', ylabel='setting2'>,
        <Axes: xlabel='s9', ylabel='setting2'>,
        <Axes: xlabel='s11', ylabel='setting2'>,
        <Axes: xlabel='s12', ylabel='setting2'>,
        <Axes: xlabel='s13', ylabel='setting2'>,
        <Axes: xlabel='s14', ylabel='setting2'>,
        <Axes: xlabel='s15', ylabel='setting2'>,
        <Axes: xlabel='s17', ylabel='setting2'>,
        <Axes: xlabel='s20', ylabel='setting2'>,
        <Axes: xlabel='s21', ylabel='setting2'>,
        <Axes: xlabel='ttf', ylabel='setting2'>],
       [<Axes: xlabel='setting1', ylabel='s2'>,
        <Axes: xlabel='setting2', ylabel='s2'>,
        <Axes: xlabel='s2', ylabel='s2'>,
        <Axes: xlabel='s3', ylabel='s2'>,
        <Axes: xlabel='s4', ylabel='s2'>,
        <Axes: xlabel='s6', ylabel='s2'>,
        <Axes: xlabel='s7', ylabel='s2'>,
        <Axes: xlabel='s8', ylabel='s2'>,
        <Axes: xlabel='s9', ylabel='s2'>,
        <Axes: xlabel='s11', ylabel='s2'>,
        <Axes: xlabel='s12', ylabel='s2'>,
        <Axes: xlabel='s13', ylabel='s2'>,
        <Axes: xlabel='s14', ylabel='s2'>,
        <Axes: xlabel='s15', ylabel='s2'>,
        <Axes: xlabel='s17', ylabel='s2'>,
        <Axes: xlabel='s20', ylabel='s2'>,
        <Axes: xlabel='s21', ylabel='s2'>,
        <Axes: xlabel='ttf', ylabel='s2'>],
       [<Axes: xlabel='setting1', ylabel='s3'>,
        <Axes: xlabel='setting2', ylabel='s3'>,
        <Axes: xlabel='s2', ylabel='s3'>,
        <Axes: xlabel='s3', ylabel='s3'>,
        <Axes: xlabel='s4', ylabel='s3'>,
        <Axes: xlabel='s6', ylabel='s3'>,
        <Axes: xlabel='s7', ylabel='s3'>,
        <Axes: xlabel='s8', ylabel='s3'>,
        <Axes: xlabel='s9', ylabel='s3'>,
        <Axes: xlabel='s11', ylabel='s3'>,
        <Axes: xlabel='s12', ylabel='s3'>,
        <Axes: xlabel='s13', ylabel='s3'>,
        <Axes: xlabel='s14', ylabel='s3'>,
        <Axes: xlabel='s15', ylabel='s3'>,
        <Axes: xlabel='s17', ylabel='s3'>,
        <Axes: xlabel='s20', ylabel='s3'>,
        <Axes: xlabel='s21', ylabel='s3'>,
        <Axes: xlabel='ttf', ylabel='s3'>],
       [<Axes: xlabel='setting1', ylabel='s4'>,
        <Axes: xlabel='setting2', ylabel='s4'>,
        <Axes: xlabel='s2', ylabel='s4'>,
        <Axes: xlabel='s3', ylabel='s4'>,
        <Axes: xlabel='s4', ylabel='s4'>,
        <Axes: xlabel='s6', ylabel='s4'>,
        <Axes: xlabel='s7', ylabel='s4'>,
        <Axes: xlabel='s8', ylabel='s4'>,
        <Axes: xlabel='s9', ylabel='s4'>,
        <Axes: xlabel='s11', ylabel='s4'>,
        <Axes: xlabel='s12', ylabel='s4'>,
        <Axes: xlabel='s13', ylabel='s4'>,
        <Axes: xlabel='s14', ylabel='s4'>,
        <Axes: xlabel='s15', ylabel='s4'>,
        <Axes: xlabel='s17', ylabel='s4'>,
        <Axes: xlabel='s20', ylabel='s4'>,
        <Axes: xlabel='s21', ylabel='s4'>,
        <Axes: xlabel='ttf', ylabel='s4'>],
       [<Axes: xlabel='setting1', ylabel='s6'>,
        <Axes: xlabel='setting2', ylabel='s6'>,
        <Axes: xlabel='s2', ylabel='s6'>,
        <Axes: xlabel='s3', ylabel='s6'>,
        <Axes: xlabel='s4', ylabel='s6'>,
        <Axes: xlabel='s6', ylabel='s6'>,
        <Axes: xlabel='s7', ylabel='s6'>,
        <Axes: xlabel='s8', ylabel='s6'>,
        <Axes: xlabel='s9', ylabel='s6'>,
        <Axes: xlabel='s11', ylabel='s6'>,
        <Axes: xlabel='s12', ylabel='s6'>,
        <Axes: xlabel='s13', ylabel='s6'>,
        <Axes: xlabel='s14', ylabel='s6'>,
        <Axes: xlabel='s15', ylabel='s6'>,
        <Axes: xlabel='s17', ylabel='s6'>,
        <Axes: xlabel='s20', ylabel='s6'>,
        <Axes: xlabel='s21', ylabel='s6'>,
        <Axes: xlabel='ttf', ylabel='s6'>],
       [<Axes: xlabel='setting1', ylabel='s7'>,
        <Axes: xlabel='setting2', ylabel='s7'>,
        <Axes: xlabel='s2', ylabel='s7'>,
        <Axes: xlabel='s3', ylabel='s7'>,
        <Axes: xlabel='s4', ylabel='s7'>,
        <Axes: xlabel='s6', ylabel='s7'>,
        <Axes: xlabel='s7', ylabel='s7'>,
        <Axes: xlabel='s8', ylabel='s7'>,
        <Axes: xlabel='s9', ylabel='s7'>,
        <Axes: xlabel='s11', ylabel='s7'>,
        <Axes: xlabel='s12', ylabel='s7'>,
        <Axes: xlabel='s13', ylabel='s7'>,
        <Axes: xlabel='s14', ylabel='s7'>,
        <Axes: xlabel='s15', ylabel='s7'>,
        <Axes: xlabel='s17', ylabel='s7'>,
        <Axes: xlabel='s20', ylabel='s7'>,
        <Axes: xlabel='s21', ylabel='s7'>,
        <Axes: xlabel='ttf', ylabel='s7'>],
       [<Axes: xlabel='setting1', ylabel='s8'>,
        <Axes: xlabel='setting2', ylabel='s8'>,
        <Axes: xlabel='s2', ylabel='s8'>,
        <Axes: xlabel='s3', ylabel='s8'>,
        <Axes: xlabel='s4', ylabel='s8'>,
        <Axes: xlabel='s6', ylabel='s8'>,
        <Axes: xlabel='s7', ylabel='s8'>,
        <Axes: xlabel='s8', ylabel='s8'>,
        <Axes: xlabel='s9', ylabel='s8'>,
        <Axes: xlabel='s11', ylabel='s8'>,
        <Axes: xlabel='s12', ylabel='s8'>,
        <Axes: xlabel='s13', ylabel='s8'>,
        <Axes: xlabel='s14', ylabel='s8'>,
        <Axes: xlabel='s15', ylabel='s8'>,
        <Axes: xlabel='s17', ylabel='s8'>,
        <Axes: xlabel='s20', ylabel='s8'>,
        <Axes: xlabel='s21', ylabel='s8'>,
        <Axes: xlabel='ttf', ylabel='s8'>],
       [<Axes: xlabel='setting1', ylabel='s9'>,
        <Axes: xlabel='setting2', ylabel='s9'>,
        <Axes: xlabel='s2', ylabel='s9'>,
        <Axes: xlabel='s3', ylabel='s9'>,
        <Axes: xlabel='s4', ylabel='s9'>,
        <Axes: xlabel='s6', ylabel='s9'>,
        <Axes: xlabel='s7', ylabel='s9'>,
        <Axes: xlabel='s8', ylabel='s9'>,
        <Axes: xlabel='s9', ylabel='s9'>,
        <Axes: xlabel='s11', ylabel='s9'>,
        <Axes: xlabel='s12', ylabel='s9'>,
        <Axes: xlabel='s13', ylabel='s9'>,
        <Axes: xlabel='s14', ylabel='s9'>,
        <Axes: xlabel='s15', ylabel='s9'>,
        <Axes: xlabel='s17', ylabel='s9'>,
        <Axes: xlabel='s20', ylabel='s9'>,
        <Axes: xlabel='s21', ylabel='s9'>,
        <Axes: xlabel='ttf', ylabel='s9'>],
       [<Axes: xlabel='setting1', ylabel='s11'>,
        <Axes: xlabel='setting2', ylabel='s11'>,
        <Axes: xlabel='s2', ylabel='s11'>,
        <Axes: xlabel='s3', ylabel='s11'>,
        <Axes: xlabel='s4', ylabel='s11'>,
        <Axes: xlabel='s6', ylabel='s11'>,
        <Axes: xlabel='s7', ylabel='s11'>,
        <Axes: xlabel='s8', ylabel='s11'>,
        <Axes: xlabel='s9', ylabel='s11'>,
        <Axes: xlabel='s11', ylabel='s11'>,
        <Axes: xlabel='s12', ylabel='s11'>,
        <Axes: xlabel='s13', ylabel='s11'>,
        <Axes: xlabel='s14', ylabel='s11'>,
        <Axes: xlabel='s15', ylabel='s11'>,
        <Axes: xlabel='s17', ylabel='s11'>,
        <Axes: xlabel='s20', ylabel='s11'>,
        <Axes: xlabel='s21', ylabel='s11'>,
        <Axes: xlabel='ttf', ylabel='s11'>],
       [<Axes: xlabel='setting1', ylabel='s12'>,
        <Axes: xlabel='setting2', ylabel='s12'>,
        <Axes: xlabel='s2', ylabel='s12'>,
        <Axes: xlabel='s3', ylabel='s12'>,
        <Axes: xlabel='s4', ylabel='s12'>,
        <Axes: xlabel='s6', ylabel='s12'>,
        <Axes: xlabel='s7', ylabel='s12'>,
        <Axes: xlabel='s8', ylabel='s12'>,
        <Axes: xlabel='s9', ylabel='s12'>,
        <Axes: xlabel='s11', ylabel='s12'>,
        <Axes: xlabel='s12', ylabel='s12'>,
        <Axes: xlabel='s13', ylabel='s12'>,
        <Axes: xlabel='s14', ylabel='s12'>,
        <Axes: xlabel='s15', ylabel='s12'>,
        <Axes: xlabel='s17', ylabel='s12'>,
        <Axes: xlabel='s20', ylabel='s12'>,
        <Axes: xlabel='s21', ylabel='s12'>,
        <Axes: xlabel='ttf', ylabel='s12'>],
       [<Axes: xlabel='setting1', ylabel='s13'>,
        <Axes: xlabel='setting2', ylabel='s13'>,
        <Axes: xlabel='s2', ylabel='s13'>,
        <Axes: xlabel='s3', ylabel='s13'>,
        <Axes: xlabel='s4', ylabel='s13'>,
        <Axes: xlabel='s6', ylabel='s13'>,
        <Axes: xlabel='s7', ylabel='s13'>,
        <Axes: xlabel='s8', ylabel='s13'>,
        <Axes: xlabel='s9', ylabel='s13'>,
        <Axes: xlabel='s11', ylabel='s13'>,
        <Axes: xlabel='s12', ylabel='s13'>,
        <Axes: xlabel='s13', ylabel='s13'>,
        <Axes: xlabel='s14', ylabel='s13'>,
        <Axes: xlabel='s15', ylabel='s13'>,
        <Axes: xlabel='s17', ylabel='s13'>,
        <Axes: xlabel='s20', ylabel='s13'>,
        <Axes: xlabel='s21', ylabel='s13'>,
        <Axes: xlabel='ttf', ylabel='s13'>],
       [<Axes: xlabel='setting1', ylabel='s14'>,
        <Axes: xlabel='setting2', ylabel='s14'>,
        <Axes: xlabel='s2', ylabel='s14'>,
        <Axes: xlabel='s3', ylabel='s14'>,
        <Axes: xlabel='s4', ylabel='s14'>,
        <Axes: xlabel='s6', ylabel='s14'>,
        <Axes: xlabel='s7', ylabel='s14'>,
        <Axes: xlabel='s8', ylabel='s14'>,
        <Axes: xlabel='s9', ylabel='s14'>,
        <Axes: xlabel='s11', ylabel='s14'>,
        <Axes: xlabel='s12', ylabel='s14'>,
        <Axes: xlabel='s13', ylabel='s14'>,
        <Axes: xlabel='s14', ylabel='s14'>,
        <Axes: xlabel='s15', ylabel='s14'>,
        <Axes: xlabel='s17', ylabel='s14'>,
        <Axes: xlabel='s20', ylabel='s14'>,
        <Axes: xlabel='s21', ylabel='s14'>,
        <Axes: xlabel='ttf', ylabel='s14'>],
       [<Axes: xlabel='setting1', ylabel='s15'>,
        <Axes: xlabel='setting2', ylabel='s15'>,
        <Axes: xlabel='s2', ylabel='s15'>,
        <Axes: xlabel='s3', ylabel='s15'>,
        <Axes: xlabel='s4', ylabel='s15'>,
        <Axes: xlabel='s6', ylabel='s15'>,
        <Axes: xlabel='s7', ylabel='s15'>,
        <Axes: xlabel='s8', ylabel='s15'>,
        <Axes: xlabel='s9', ylabel='s15'>,
        <Axes: xlabel='s11', ylabel='s15'>,
        <Axes: xlabel='s12', ylabel='s15'>,
        <Axes: xlabel='s13', ylabel='s15'>,
        <Axes: xlabel='s14', ylabel='s15'>,
        <Axes: xlabel='s15', ylabel='s15'>,
        <Axes: xlabel='s17', ylabel='s15'>,
        <Axes: xlabel='s20', ylabel='s15'>,
        <Axes: xlabel='s21', ylabel='s15'>,
        <Axes: xlabel='ttf', ylabel='s15'>],
       [<Axes: xlabel='setting1', ylabel='s17'>,
        <Axes: xlabel='setting2', ylabel='s17'>,
        <Axes: xlabel='s2', ylabel='s17'>,
        <Axes: xlabel='s3', ylabel='s17'>,
        <Axes: xlabel='s4', ylabel='s17'>,
        <Axes: xlabel='s6', ylabel='s17'>,
        <Axes: xlabel='s7', ylabel='s17'>,
        <Axes: xlabel='s8', ylabel='s17'>,
        <Axes: xlabel='s9', ylabel='s17'>,
        <Axes: xlabel='s11', ylabel='s17'>,
        <Axes: xlabel='s12', ylabel='s17'>,
        <Axes: xlabel='s13', ylabel='s17'>,
        <Axes: xlabel='s14', ylabel='s17'>,
        <Axes: xlabel='s15', ylabel='s17'>,
        <Axes: xlabel='s17', ylabel='s17'>,
        <Axes: xlabel='s20', ylabel='s17'>,
        <Axes: xlabel='s21', ylabel='s17'>,
        <Axes: xlabel='ttf', ylabel='s17'>],
       [<Axes: xlabel='setting1', ylabel='s20'>,
        <Axes: xlabel='setting2', ylabel='s20'>,
        <Axes: xlabel='s2', ylabel='s20'>,
        <Axes: xlabel='s3', ylabel='s20'>,
        <Axes: xlabel='s4', ylabel='s20'>,
        <Axes: xlabel='s6', ylabel='s20'>,
        <Axes: xlabel='s7', ylabel='s20'>,
        <Axes: xlabel='s8', ylabel='s20'>,
        <Axes: xlabel='s9', ylabel='s20'>,
        <Axes: xlabel='s11', ylabel='s20'>,
        <Axes: xlabel='s12', ylabel='s20'>,
        <Axes: xlabel='s13', ylabel='s20'>,
        <Axes: xlabel='s14', ylabel='s20'>,
        <Axes: xlabel='s15', ylabel='s20'>,
        <Axes: xlabel='s17', ylabel='s20'>,
        <Axes: xlabel='s20', ylabel='s20'>,
        <Axes: xlabel='s21', ylabel='s20'>,
        <Axes: xlabel='ttf', ylabel='s20'>],
       [<Axes: xlabel='setting1', ylabel='s21'>,
        <Axes: xlabel='setting2', ylabel='s21'>,
        <Axes: xlabel='s2', ylabel='s21'>,
        <Axes: xlabel='s3', ylabel='s21'>,
        <Axes: xlabel='s4', ylabel='s21'>,
        <Axes: xlabel='s6', ylabel='s21'>,
        <Axes: xlabel='s7', ylabel='s21'>,
        <Axes: xlabel='s8', ylabel='s21'>,
        <Axes: xlabel='s9', ylabel='s21'>,
        <Axes: xlabel='s11', ylabel='s21'>,
        <Axes: xlabel='s12', ylabel='s21'>,
        <Axes: xlabel='s13', ylabel='s21'>,
        <Axes: xlabel='s14', ylabel='s21'>,
        <Axes: xlabel='s15', ylabel='s21'>,
        <Axes: xlabel='s17', ylabel='s21'>,
        <Axes: xlabel='s20', ylabel='s21'>,
        <Axes: xlabel='s21', ylabel='s21'>,
        <Axes: xlabel='ttf', ylabel='s21'>],
       [<Axes: xlabel='setting1', ylabel='ttf'>,
        <Axes: xlabel='setting2', ylabel='ttf'>,
        <Axes: xlabel='s2', ylabel='ttf'>,
        <Axes: xlabel='s3', ylabel='ttf'>,
        <Axes: xlabel='s4', ylabel='ttf'>,
        <Axes: xlabel='s6', ylabel='ttf'>,
        <Axes: xlabel='s7', ylabel='ttf'>,
        <Axes: xlabel='s8', ylabel='ttf'>,
        <Axes: xlabel='s9', ylabel='ttf'>,
        <Axes: xlabel='s11', ylabel='ttf'>,
        <Axes: xlabel='s12', ylabel='ttf'>,
        <Axes: xlabel='s13', ylabel='ttf'>,
        <Axes: xlabel='s14', ylabel='ttf'>,
        <Axes: xlabel='s15', ylabel='ttf'>,
        <Axes: xlabel='s17', ylabel='ttf'>,
        <Axes: xlabel='s20', ylabel='ttf'>,
        <Axes: xlabel='s21', ylabel='ttf'>,
        <Axes: xlabel='ttf', ylabel='ttf'>]], dtype=object)

3.3 Principal Component Analysis

# SCikit-learn modules required for PCA
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler

train = pd.read_csv('train.csv')

col_to_analyze = ['setting1','setting2','setting3','s1','s2','s3','s4','s5','s6','s7','s8','s9','s10','s11',
                  's12','s13','s14','s15','s16','s17','s18','s19','s20','s21']

df_PCA = train[col_to_analyze]
target = train['label_mcc']
target2 = train['ttf']

# Normlization of the features
scaler = StandardScaler()
X_scaled = scaler.fit_transform(df_PCA)

# PCA instanciation on 8 components
n_components = 8
pca = PCA(n_components=n_components)
pca.fit(X_scaled)

PCA(n_components=8)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

# Cumulative variance calculation
scree = (pca.explained_variance_ratio_*100).round(2)
scree_cum = scree.cumsum().round()
axe_x = np.arange(1, len(scree_cum)+1)

plt.figure(figsize=(10,6))
plt.bar(axe_x, scree, color='steelblue')
plt.plot(axe_x, scree_cum, c='red',marker='o')
plt.xlabel("Number of components retained")
plt.ylabel("Explained Variance (%)")
plt.title("Scree Plot - Optimal Component Number Detection")
plt.xticks(np.arange(1,9,1))
plt.show(block=False)
plt.show

<function matplotlib.pyplot.show(close=None, block=None)>

# Tracé d'un tableau heatmap sur les différentes composantes. 
pcs = pca.components_
x_axis_labels=['Component_1', 'Component_2', 'Component_3', 'Component_4', 'Component_5', 'Component_6', 
               'Component_7', 'Component_8']
fig, ax = plt.subplots(figsize=(20, 6))
sns.heatmap(pcs.T, vmin=-1, vmax=1, annot=True, cmap="coolwarm", fmt="0.2f", yticklabels=col_to_analyze, 
            xticklabels=x_axis_labels)
plt.title('Heatmap showing the composition of the different components of the PCA')

Text(0.5, 1.0, 'Heatmap showing the composition of the different components of the PCA')

X_proj = pca.transform(X_scaled)

palette_colors = ["green", "orange", "red"]
legend_labels = {0: "Normal condition", 1: "Low risk of failure", 2: "High risk of failure"}
target_mapped = [legend_labels[t] for t in target]
plt.figure(figsize=(8,8))
sns.scatterplot(x=X_proj[:,0], y=X_proj[:,1], alpha=0.2, hue=target_mapped, palette=palette_colors)
plt.show()

import matplotlib.colors as mcolors

# Ensure target2 is a continuous variable
# ...

plt.figure(figsize=(8, 8))

# Create the scatter plot
scatter = sns.scatterplot(
    x=X_proj[:, 0], 
    y=X_proj[:, 1], 
    alpha=0.2, 
    hue=target2, 
    palette='magma'
)

# Create a normalizer object which will map the values of target2 to the range [0, 1]
norm = mcolors.Normalize(vmin=target2.min(), vmax=target2.max())

# Create a ScalarMappable and initialize with the norm object and the chosen colormap
sm = plt.cm.ScalarMappable(cmap="magma", norm=norm)
sm.set_array([])

# Add the color bar using the ScalarMappable
plt.colorbar(sm)

plt.show()

# Créer un DataFrame pour Plotly (si vos données ne sont pas déjà dans un DataFrame)
import pandas as pd
df = pd.DataFrame({
    'Composant 1': X_proj[:, 0],
    'Composant 2': X_proj[:, 1],
    'Composant 3': X_proj[:, 2],
    'Target': target
})

color_discrete_map = {'0': 'rgb(255,0,0)', '1': 'rgb(0,255,0)', '2': 'rgb(0,0,255)'}
# Création du graphique 3D
fig = px.scatter_3d(df, x='Composant 1', y='Composant 2', z='Composant 3',
                    color='Target',
                    color_discrete_map=color_discrete_map,
                    opacity=0.5) 

# Mise à jour des légendes et titres
fig.update_layout(legend_title="New Legend Title",
                  scene=dict(
                      xaxis_title='Composant 1',
                      yaxis_title='Composant 2',
                      zaxis_title='Composant 3'
                  ))
fig.update_traces(marker_size=2)
fig.update(layout_coloraxis_showscale=False)

fig.show()

3.4 EDA Summary:

• There is a very high correlation (> 0.8) between some features e.g.(s14 & s9), (s11 & s4), (s11 & s7), (s11 & s12), (s4 & s12), (s8 & s13), (s7 & s12). This multicollinearity may hurt the performance of some machine learning algorithms. So, part of these features will be target for elimination in feature selection during the modeling phase.
• Most features have nonlinear relation with the TTF, hence adding their polynomial transforms may enhance models performance.
• Most features exhibit normal distribution which is likely improves models performance.
• AUC ROC should be used for classification models evaluation instead of Accuracy due to class’s imbalance in the training data.